Actually it is clear as long as you remember that main point you made: debit and credit just means left and right.

We are all spoiled by thinking of debit/credit as equal to decrease/increase respectively because that how we interpret our bank accounts. That understanding totally collides with formal accounting where debit/credit DON'T mean decrease/increase respectively. I think this is the root cause of all confusion about double-entry accounting. I may be wrong about this, happy to be corrected but that is the bit my brain grinds against when trying to make sense of things.

E.g. I replaced all instance of debit with "Left" and credit with "Right" in your example:

    1. Merchant takes out a loan for $5,000 and receives $5,000 in cash. • Assets (Cash) increase by $5,000 (Left). • Liabilities (Loan Payable) increase by $5,000 (Right). • Equity remains unchanged.

    2. Merchant buys inventory for $1,000 cash. • Assets (Cash) decrease by $1,000 (Right). • Assets (Inventory) increase by $1,000 (Left). • Total assets remain unchanged, and liabilities and equity are unaffected.

    3. Merchant sells all inventory for $1,500 cash. • Assets (Cash) increase by $1,500 (Left). • Assets (Inventory) decrease by $1,000 (Right) (recording cost of goods sold). • Equity (Retained Earnings) increases by $500 (Right), representing the profit ($1,500 sales - $1,000 cost).

    4. Customer1 deposits $500 in cash for future delivery of goods. • Assets (Cash) increase by $500 (Left). • Liabilities (Unearned Revenue) increase by $500 (Right). • Equity remains unchanged.

    5. Customer1 transfers half of the future delivery of goods to Customer2. • No changes to assets, liabilities, or equity occur at this point. The merchant’s obligation to deliver goods (reflected as Unearned Revenue) is still $500 but now split between two customers (Customer1 and Customer2). Internal tracking of this obligation may be updated, but the total financial liability remains the same.

I find this much more easier to reason with.

Yes exactly. With assets liabilities and equity having a left and right entry, they were following the convention when posting a journal entry to the ledger, left entries must equal right entries. (Debits must equal credits). Because A=L+E, we get assets to the left and liabilities to the right.

Appreciate your confirmation. If you have any blog about double entry accounting (or accounting in general), I'll be interested to read it. I have nothing to do with accounting in my professional life but I've always been curious about it.

I like this free site written by a CPA. https://www.accountingverse.com/

I understand this. But we’re talking about computers, not Italian merchants. Italian merchants had actual pieces of paper. Computers have tables and views and frontends that are separate from the tables.

Any self-respecting accounting system should be able to produce a balance sheet that matches the conventions you’re describing. I don’t think it follows that the actual numbers in the database that get summed to produce the total liabilities should be positive.

I've often wondered about this in the shower. Why debits and credits, when we can just make income negative and let everything sum to 0? Then you can track the balance for each account in a single field in the database.

And the answer is that "0" first entered Europe around the time they invented double-entry bookkeeping there. Negative numbers reached Europe centuries after that.

I showed the internals of a number-line-based accounting systems to an accountant once, and he was so confused by the negative incomes.

https://en.wikipedia.org/wiki/Negative_number#History

https://en.wikipedia.org/wiki/Double-entry_bookkeeping#Histo...

I think we are talking about two different things. Yes, of course you can build an accounting system using whatever database algorithm and programming framework you like. But your users expect debits and credits and A=LE or A-L=E because that’s what their auditors expect.

In the scenario four I presented earlier, I believe it is intuitive to think of unearned revenue (liability) as a positive number. When the customer picks up the order, the unearned revenue will be transferred to equity.

Thank you for an example. But I don't see how it explains why debit/credit should be used instead of simple signed amount. Like how Transaction(from, to) where `from` and `to` are Entry(account, credit|debit, unsigned amount) make things easier than Entry(account, signed amount).

You basically used different labels for positive or negative amount in the example.

The story I was told and what I believe is that the journal entry is and always is the source of truth. A merchant may have several journals. A separate one for each line of business and maintained by separate clerks. The different journals would then be consolidated into a single ledger. So he can tell what his equity is. When transferring the journal entry to A=L+E. Those early accountants used their version of Excel. For Assets, They took a page and drew a vertical line. For Liabilities, they also drew a vertical line. Same for equity. They called the left side debit and the right side credit. We don’t know why the Italians named it this way. We can only assume the first ledgers dealt with paying down amounts of credit they owed others. Anyways this early “excel” allowed simple ledgers to have two columns. Positive asset changes go to the left and negative to the right. Positive liabilities changes to the right and negative changes to the left. Same thing for equity. I assume this was mantra they told themselves to ensure correctness or reconciliation. When transferring a journal entry to the ledger there must be a debit and a credit or there is fraud. For example an unscrupulous clerk may have taken a loan out. The journal entry may not tell where that money went. When transferring to the ledger, the loan would be entered as a credit. Because the there was not a corresponding debit, either an increase in cash assets or decrease in equity. The balance would have been off and would have told the merchant something was wrong.

Money can't appear and disappear. There should be always a destination. It helps accounting a lot. If someone owes anyone, liabilities increases (active/passive accounts), but this liability is spent somehow, which could become an asset (Goods Purchased using a Loan), so you can track all the chain through account statements.

Destination is the key. You can't just arbitrarily change an account balance using a transaction in a ledger. There should be a destination and this the second record.

This what GAAP, IFRS and even all the Basels for banks describe in strict detail. But every accounting system and practice is based on double entry and not just keeps the balance sheet consistent but adds a meaning to every transaction using predefined types of accounts.

I think you missed the fact my model is equivalent to double entry as it understood by financial organisations. The only change is a direction (debit or credit) bit replaced with a sign bit. All other info including accounts to correctly track money flow are still there.

I think that's because double entry bookkeeping precedes the concept of negative numbers. To be more precise, double entry bookkeeping was invented by people who had not yet been introduced to negative numbers.

At least that's how it's been explained to me.

As someone pointed out just below, you do not need two rows. You can have one row: (amount, credit_account, debit_account).

The article does talk about a bit why using negative amounts for this is a bad idea.